Are legislators responsive to their constituents in their public communication? To what extent are they able to shape the agenda that the mass public cares about, as expressed by the issues they discuss? We address this twofold question with an analysis of all tweets sent by Members of the U.S. Congress and a random sample of their followers from January 2013 to March 2014. Using a Latent Dirichlet Allocation model, we extract topics that represent the diversity of issues that legislators and ordinary citizens discuss on this social networking site. Then, we exploit variation in the distribution of topics over time to test whether Members of Congress lead or follow their constituents in their selection of issues to discuss, employing a Granger-causality framework. We find that legislators are responsive in their public statements to their constituents, but also that they have limited influence on their followers’ public agenda. To further understand the mechanisms that explain political responsiveness, we also examine whether Members of Congress are more responsive to specific constituents groups, showing that they are more influenced by co-partisans, politically interested citizens, and social media users located within their constituency. 